Honors Calculus: Ch 5A Review/Practice Test
Indefinite Integration
Name_______________________________
Date__________________________
Multiple-Choice – Circle the correct answer. You may receive partial credit if you show your
work.
1. Rewrite the integrand then evaluate
⎛
∫ ⎜⎝ x
−4
+
1 ⎞
⎟dx
6 x⎠
1
2 32
+
x +C
3x 3 3
€
1
1 12
b. − 3 + x + C
3x
3
1
1 3
c. − 4 + x 2 + C
3x
3
1
1 1
d. − 3 + x 2 + C
4x
3
a. −
€
€
€
2.€ Use U-substitution to integrate
a.
b.
€
c.
€
d.
€
€
€
€
4
5
5
− 3) dx
6
1 5
x − 3) +€
C
(
30
6
1 5
x − 3) + C
(
6
1 30
( x − 3) + C
30
6
1
− ( x 5 − 3) + C
6
€
3. Use U-substitution to integrate
€
5
+C
(7 − x ) 5
€
1
b.
5 +C
5( 7 − x )
1
c. −
5 +C
5( 7 − x )
6
+C
d.
(7 − x ) 7
a.
∫ x (x
1
∫ (7 − x )
6
dx
4.
1
∫ sin (5x ) dx
2
a.
€
b.
€
€
€
c.
d.
e.
1
cot 5x + C
5
1 3
csc 5x + C
3
−cot 5x csc5x + C
1
− cot 5x + C
5
1
− csc 3 5x + C
3
€
5. Use U-substitution to integrate
€
€
€
∫ csc6θ cot 6θ dθ
1
a. − csc6θ + C
6
€
1
b.
csc6θ + C
6
1
c. − cot 6θ + C
6
1
d.
cot 6θ + C
6
€
€
Open-Response
– Show your work.
6. Find the integral of the following algebraic expressions.
⎛
2⎞
∫ ⎜⎝1+ 3x 2 − x 2 ⎟⎠ dx
€
7. Find the integral of each of the following expressions.
cos x
(3x - 2) 2
b. ∫
dx
dx
a. ∫
sin 2 x
x
€
€
c.
∫e
4 t −3
dt
€
d.
∫
x 2 − 3x + 2
dx
x
€
e.
∫ 5 dx
x
€
f.
∫ −2sin x dx
€
9. Solve the following differential equation. (In other words find f (x) .)
f ʹ ( x ) = 10, f ʹ( −2) = −17, f (1) = 6
€
€
10. Use U-substitution to integrate each of the following expressions.
4
a. ∫ ( 3x − 2) dx
b. ∫ −2x 9 − x 2 dx
€
€
c.
€
∫ sec 3x tan 3x dx
d.
€
∫ sin x
cos x dx